Multiplicative forms at the infinitesimal level

Abstract: We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known integration results related to Poisson geometry. We also revisit multiplicative multivector fields and their infinitesimal counterparts, drawing a parallel between the two theories.